Question

The total number of words which can be formed using all the letters of the word "AKSHI" if each word begins with vowel or terminates with vowel -

• A. 84
• B. 12
• C. 48
• D. 60

Answer 1

Answer: (A)

Total possible words - words do not begin or terminate with vowel
Total words $=5!=120$
Words which do not begin and terminate with vowel $=33212=36$
Desired words : $180-36=84$
II-Method $\to$ words which begin with vowel $(A/l)=4!2=48$ ways $\to$ say $=n(A)$
Similarly words terminating with vowel
$=4!2=48\text{ ways }\to \text{ say }=n(B)$
Now exclude words which begin as well as terminates with vowel
$23211$ ways $\to n(A\cap B)$
Desired number of words :-
$48+48-12=84$ ways
$(\because n(A\cup B)=n(A)+n(B)-n(A\cap B))$